Problem III Let B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B +3I, where I is the identity matrix. 41. 10 (9) 0 1 0 10 /1 0 1\ 101 42. 030 10 /1 0 1 43. 0 (-1) 46- 0 44. 01 (0 0 0) 1 0 1 0-20 1 01 000\
Problem III Let B denote the matrix given below. (i) Find all eigenvalues of the matrix B. (ii) For each eigenvalue of B, find an associated eigenvector. (iii) Is the matrix B diagonalizable? Explain. (iv) Find all eigenvalues of the matrix 2B +3I, where I is the identity matrix. 41. 10 (9) 0 1 0 10 /1 0 1\ 101 42. 030 10 /1 0 1 43. 0 (-1) 46- 0 44. 01 (0 0 0) 1 0 1 0-20 1 01 000\
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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42 please
Transcribed Image Text:Problem III Let B denote the matrix given below.
(i) Find all eigenvalues of the matrix B.
(ii) For each eigenvalue of B, find an associated eigenvector.
(iii) Is the matrix B diagonalizable? Explain.
(iv) Find all eigenvalues of the matrix 2B + 31, where I is the identity matrix.
41.
45.
49.
53.
57.
1 0 1
010
10 1
1
-3 0
0 1
000
3
1
01 0
0 1
1 02
000
201
030
102
42.
46.
50.
54.
10
030
101
101
020
101
000
102
020
02
20 -1
00
20 -1
0
2
58. 0
-1 0
43. 0
47.
51.
1 0
-1
1 0 1
55.
000
1 0 1
01
0
0
0
302
020
-1 0
1
02
0
10 -1
20-2
59. -1 1
2
10 -1
1
44. 0
1
48.
52.
56.
60.
0
-20
0
00
201
010
010
101
000
0
02
-1 0
2 -1
0
1
2
0
1
1
0
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